/*

	doc: http://www.vni.com/corner/garage/grande/api/com/imsl/math/Complex.htm
	
 * -------------------------------------------------------------------------
 *	$Id: JMath.java,v 1.1 2003/02/10 23:07:09 augustbering Exp $
 * -------------------------------------------------------------------------
 *	Copyright (c) 1999 Visual Numerics Inc. All Rights Reserved.
 *
 * Permission to use, copy, modify, and distribute this software is freely
 * granted by Visual Numerics, Inc., provided that the copyright notice
 * above and the following warranty disclaimer are preserved in human
 * readable form.
 *
 * Because this software is licenses free of charge, it is provided
 * "AS IS", with NO WARRANTY.  TO THE EXTENT PERMITTED BY LAW, VNI
 * DISCLAIMS ALL WARRANTIES, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED
 * TO ITS PERFORMANCE, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
 * VNI WILL NOT BE LIABLE FOR ANY DAMAGES WHATSOEVER ARISING OUT OF THE USE
 * OF OR INABILITY TO USE THIS SOFTWARE, INCLUDING BUT NOT LIMITED TO DIRECT,
 * INDIRECT, SPECIAL, CONSEQUENTIAL, PUNITIVE, AND EXEMPLARY DAMAGES, EVEN
 * IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGES. 
 *
 *
 * This Java code is based on C code in the package fdlibm,
 * which can be obtained from www.netlib.org.
 * The original fdlibm C code contains the following notice.
 *
 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
 *
 * Developed at SunSoft, a Sun Microsystems, Inc. business.
 * Permission to use, copy, modify, and distribute this
 * software is freely granted, provided that this notice 
 * is preserved.
 *
 *--------------------------------------------------------------------------
 */
package myjava;

import java.util.Random;
/*
 *	Pure Java implementation of the standard java.lang.Math class.
 *	This Java code is based on C code in the package fdlibm,
 *	which can be obtained from www.netlib.org.
 *
 *	@author Sun Microsystems (original C code in fdlibm)
 *	@author	John F. Brophy (translated from C to Java)
 */
public final class Math
{
	static public final double PI = Double.longBitsToDouble(0x400921fb54442d18L);  /* 3.14159265358979323846 */
	static public final double E  = 2.7182818284590452354;

	static private Random random;


	/**
	 *	Returns the absolute value of its argument.
	 *	@param	x	The argument, an integer.
	 *	@return	Returns |x|.
	 */
	strictfp public static int abs(int x)
	{
		return ((x < 0) ? -x : x);
    }

	
	/**
	 *	Returns the absolute value of its argument.
	 *	@param	x	The argument, a long.
	 *	@return	Returns |x|.
	 */
	strictfp public static long abs(long x)
	{
		return ((x < 0L) ? -x : x);
    }

	
	/**
	 *	Returns the absolute value of its argument.
	 *	@param	x	The argument, a float.
	 *	@return	Returns |x|.
	 */
	strictfp public static float abs(float x)
	{
		return ((x <= 0.0f) ? 0.0f-x : x);
    }

	
	/**
	 *	Returns the absolute value of its argument.
	 *	@param	x	The argument, a double.
	 *	@return	Returns |x|.
	 */
	strictfp public static double abs(double x)
	{
		return ((x <= 0.0) ? 0.0-x : x);
    }

	
	/**
	 *	Returns the smaller of its two arguments.
	 *	@param	x	The first argument, an integer.
	 *	@param	y	The second argument, an integer.
	 *	@return	Returns the smaller of x and y.
	 */
	strictfp public static int min(int x, int y)
	{
		return ((x < y) ? x : y);
    }

	
	/**
	 *	Returns the smaller of its two arguments.
	 *	@param	x	The first argument, a long.
	 *	@param	y	The second argument, a long.
	 *	@return	Returns the smaller of x and y.
	 */
	strictfp public static long min(long x, long y)
	{
		return ((x < y) ? x : y);
    }

	
	/**
	 *	Returns the smaller of its two arguments.
	 *	@param	x	The first argument, a float.
	 *	@param	y	The second argument, a float.
	 *	@return	Returns the smaller of x and y.
	 *			This function considers -0.0f to
	 *			be less than 0.0f.
	 */
	strictfp public static float min(float x, float y)
	{
		if (Float.isNaN(x))  return x;
		float ans = ((x <= y) ? x : y);
		if (ans == 0.0f &&
			Float.floatToIntBits(y) == 0x80000000)
				ans = y;
		return ans;
    }


	/**
	 *	Returns the smaller of its two arguments.
	 *	@param	x	The first argument, a double.
	 *	@param	y	The second argument, a double.
	 *	@return	Returns the smaller of x and y.
	 *			This function considers -0.0 to
	 *			be less than 0.0.
	 */	strictfp public static double min(double x, double y)
	{
		if (Double.isNaN(x))  return x;
		double ans = ((x <= y) ? x : y);
		if (x == 0.0  &&  y == 0.0  &&
			Double.doubleToLongBits(y) == 0x8000000000000000L)
				ans = y;
		return ans;
    }

	
	/**
	 *	Returns the larger of its two arguments.
	 *	@param	x	The first argument, an integer.
	 *	@param	y	The second argument, an integer.
	 *	@return	Returns the larger of x and y.
	 */
	strictfp public static int max(int x, int y)
	{
		return ((x > y) ? x : y);
    }

	
	/**
	 *	Returns the larger of its two arguments.
	 *	@param	x	The first argument, a long.
	 *	@param	y	The second argument, a long.
	 *	@return	Returns the larger of x and y.
	 */
	strictfp public static long max(long x, long y)
	{
		return ((x > y) ? x : y);
    }

	
	/**
	 *	Returns the larger of its two arguments.
	 *	@param	x	The first argument, a float.
	 *	@param	y	The second argument, a float.
	 *	@return	Returns the larger of x and y.
	 *			This function considers -0.0f to
	 *			be less than 0.0f.
	 */
	strictfp public static float max(float x, float y)
	{
		if (Float.isNaN(x))  return x;
		float ans = ((x >= y) ? x : y);
		if (ans == 0.0f &&  Float.floatToIntBits(x) == 0x80000000)
			ans = y;
		return ans;
    }


	/**
	 *	Returns the larger of its two arguments.
	 *	@param	x	The first argument, a double.
	 *	@param	y	The second argument, a double.
	 *	@return	Returns the larger of x and y.
	 *			This function considers -0.0 to
	 *			be less than 0.0.
	 */
	strictfp public static double max(double x, double y)
	{
		if (Double.isNaN(x))  return x;
		double ans = ((x >= y) ? x : y);
		if (x == 0.0  &&  y == 0.0  &&  Double.doubleToLongBits(x) == 0x8000000000000000L)
			ans = y;
		return ans;
    }


	/**
	 *	Returns the integer closest to the arguments.
	 *	@param	x	The argument, a float.
	 *	@return	Returns the integer closest to x.
	 */
	strictfp public static int round(float x)
	{
		return (int)floor(x+0.5f);
    }


	/**
	 *	Returns the long closest to the arguments.
	 *	@param	x	The argument, a double.
	 *	@return	Returns the long closest to x.
	 */
	strictfp public static long round(double x)
	{
		return (long)floor(x+0.5);
    }

	
	/**
	 *	Returns the random number.
	 *	@return	Returns a random number from a uniform distribution.
	 */
    synchronized strictfp public static double random()
	{
        if (random == null)  random = new Random();
        return random.nextDouble();
    }


	/*
	 *	This following code is derived from fdlibm, which contained
	 *	the following notice.
	 * ====================================================
	 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
	 *
	 * Developed at SunSoft, a Sun Microsystems, Inc. business.
	 * Permission to use, copy, modify, and distribute this
	 * software is freely granted, provided that this notice 
	 * is preserved.
	 * ====================================================
	 *
	 * Constants:
	 * The hexadecimal values are the intended ones for the following
	 * constants. The decimal values may be used, provided that the
	 * compiler will convert from decimal to binary accurately enough
	 * to produce the hexadecimal values shown.
	 */

	static private final double huge   = 1.0e+300;
	static private final double tiny   = 1.0e-300;


	/**
	 *	Returns the value of its argument rounded toward
	 *	positive infinity to an integral value.
	 *	@param	x	The argument, a double.
	 *	@return	Returns the smallest double, not less than x,
	 *			that is an integral value.
	 */
	static public double ceil(double x)
	{
		int		exp, sign;
		long	ix;

		if (x == 0)  return x;

		ix = Double.doubleToLongBits(x);
		sign = (int)((ix>>63)&1);
		exp = ((int)(ix>>52)&0x7ff) - 0x3ff;

		if (exp < 0) {
			if (x < 0.0)
				return NEGATIVE_ZERO;
			else if (x == 0.0)
				return x;
			else
				return 1.0;
		} else if (exp < 53) {
			long mask = (0x000fffffffffffffL>>>exp);
			if ((mask&ix) == 0)  return x;  // x is integral
			if (x > 0.0)
				ix += 0x0010000000000000L>>exp;
			ix = ix & (~mask);
		} else if (exp == 1024) { // infinity
			return x;
		}

		return Double.longBitsToDouble(ix);
	}

	/**
	 *	Returns the value of its argument rounded toward
	 *	negative infinity to an integral value.
	 *	@param	x	The argument, a double.
	 *	@return	Returns the smallest double, not greater than x,
	 *			that is an integral value.
	 */
	static public double floor(double x)
	{
		int		exp, sign;
		long	ix;

		if (x == 0)  return x;

		ix = Double.doubleToLongBits(x);
		sign = (int)((ix>>63)&1);
		exp = ((int)(ix>>52)&0x7ff) - 0x3ff;

		if (exp < 0) {
			if (x < 0.0)
				return -1.0;
			else if (x == 0.0)
				return x;
			else
				return 0.0;
		} else if (exp < 53) {
			long mask = (0x000fffffffffffffL>>>exp);
			if ((mask&ix) == 0)  return x;  // x is integral
			if (x < 0.0)
				ix += 0x0010000000000000L>>exp;
			ix = ix & (~mask);
		} else if (exp == 1024) { // infinity
			return x;
		}

		return Double.longBitsToDouble(ix);
	}

		
		
	static private final double TWO52[] = {
		Double.longBitsToDouble(0x4330000000000000L),  /*  4.50359962737049600000e+15 */
		Double.longBitsToDouble(0xc330000000000000L)   /* -4.50359962737049600000e+15 */
	};

	static private final double NEGATIVE_ZERO = Double.longBitsToDouble(0x8000000000000000L);


	/**
	 *	Returns the value of its argument rounded toward
	 *	the closest integral value.
	 *	@param	x	The argument, a double.
	 *	@return	Returns the double closest to x
	 *			that is an integral value.
	 */
	static public double rint(double x)
	{
		int		exp, sign;
		long	ix;
		double	w;

		if (x == 0)  return x;

		ix = Double.doubleToLongBits(x);
		sign = (int)((ix>>63)&1);
		exp = ((int)(ix>>52)&0x7ff) - 0x3ff;

		if (exp < 0) {
			if (x < -0.5)
				return -1.0;
			else if (x > 0.5)
				return 1.0;
			else if (sign == 0)
				return 0.0;
			else
				return NEGATIVE_ZERO;
		} else if (exp < 53) {
			long mask = (0x000fffffffffffffL>>>exp);
			if ((mask&ix) == 0)  return x;  // x is integral
		} else if (exp == 1024) { // infinity
			return x;
		}

		x = Double.longBitsToDouble(ix);
		w = TWO52[sign] + x;
		return w - TWO52[sign];
	}


	/**
	 *	Returns  x REM p =  x - [x/p]*p as if in infinite 
	 * 	precise arithmetic, where [x/p] is the (infinite bit) 
	 *	integer nearest x/p (in half way case choose the even one).
	 *	@param	x	The dividend.
	 *	@param	y	The divisor.
	 *	@return	The remainder computed according to the IEEE 754 standard.
	 */
	static public double IEEEremainder(double x, double p)
	{
		int		hx,hp;
		int		sx,lx,lp;// unsigned
		double	p_half;

		hx = __HI(x);		/* high word of x */
		lx = __LO(x);		/* low  word of x */
		hp = __HI(p);		/* high word of p */
		lp = __LO(p);		/* low  word of p */
		sx = hx&0x80000000;
		hp &= 0x7fffffff;
		hx &= 0x7fffffff;

		/* purge off exception values */
		if ((hp|lp) == 0)  return (x*p)/(x*p); 	/* p = 0 */
		
		if ((hx >= 0x7ff00000) ||			/* x not finite */
			((hp >= 0x7ff00000)&&			/* p is NaN */
			(((hp-0x7ff00000)|lp)!=0)))
			return (x*p)/(x*p);
		
		if (hp <= 0x7fdfffff)  x = x%(p+p);		/* now x < 2p */

		if (((hx-hp)|(lx-lp)) == 0)	return zero*x;

		x  = abs(x);
		p  = abs(p);
		if (hp < 0x00200000) {
			if (x+x > p) {
				x -= p;
				if (x+x >= p) x -= p;
			}
		} else {
			p_half = 0.5*p;
			if (x > p_half) {
				x -= p;
				if (x >= p_half)
					x -= p;
			}
		}
		lx = __HI(x);
		lx ^= sx;
		return setHI(x, lx);
	}



    /* sqrt(x)
     * Return correctly rounded sqrt.
     *   ------------------------------------------
     *   |  Use the hardware sqrt if you have one |
     *   ------------------------------------------
     * Method: 
     *   Bit by bit method using integer arithmetic. (Slow, but portable) 
     *   1. Normalization
     *  Scale x to y in [1,4) with even powers of 2: 
     *  find an integer k such that  1 <= (y=x*2^(2k)) < 4, then
     *      sqrt(x) = 2^k * sqrt(y)
     *   2. Bit by bit computation
     *  Let q  = sqrt(y) truncated to i bit after binary point (q = 1),
     *       i                                                   0
     *                             i+1         2
     *      s  = 2*q , and  y  =  2   * ( y - q  ).     (1)
     *       i      i            i                 i
     *                                                        
     *  To compute q    from q , one checks whether 
     *              i+1       i                       
     *
     *                -(i+1) 2
     *          (q + 2      ) <= y.         (2)
     *                i
     *                         -(i+1)
     *  If (2) is false, then q   = q ; otherwise q   = q  + 2      .
     *                         i+1   i             i+1   i
     *
     *  With some algebric manipulation, it is not difficult to see
     *  that (2) is equivalent to 
     *                             -(i+1)
     *          s  +  2       <= y          (3)
     *           i                i
     *
     *  The advantage of (3) is that s  and y  can be computed by 
     *                    i      i
     *  the following recurrence formula:
     *      if (3) is false
     *
     *      s     =  s  ,   y    = y   ;            (4)
     *       i+1      i      i+1    i
     *
     *      otherwise,
     *                     -i                      -(i+1)
     *      s     =  s  + 2  ,  y    = y  -  s  - 2         (5)
     *       i+1      i          i+1    i     i
     *              
     *  One may easily use induction to prove (4) and (5). 
     *  Note. Since the left hand side of (3) contain only i+2 bits,
     *        it does not necessary to do a full (53-bit) comparison 
     *        in (3).
     *   3. Final rounding
     *  After generating the 53 bits result, we compute one more bit.
     *  Together with the remainder, we can decide whether the
     *  result is exact, bigger than 1/2ulp, or less than 1/2ulp
     *  (it will never equal to 1/2ulp).
     *  The rounding mode can be detected by checking whether
     *  huge + tiny is equal to huge, and whether huge - tiny is
     *  equal to huge for some floating point number "huge" and "tiny".
     *
     *      
     * Special cases:
     *  sqrt(+-0) = +-0     ... exact
     *  sqrt(inf) = inf
     *  sqrt(-ve) = NaN     ... with invalid signal
     *  sqrt(NaN) = NaN     ... with invalid signal for signaling NaN
     */

	/**
	 *	Returns the square root of its argument.
	 *	@param	x	The argument, a double.
	 *	@return	Returns the square root of x.
	 */
	static public double sqrt(double x)
	{
		long ix = Double.doubleToLongBits(x);
		
		/* take care of Inf and NaN */
		if ((ix&0x7ff0000000000000L)==0x7ff0000000000000L) {
			/* sqrt(NaN)=NaN, sqrt(+inf)=+inf  sqrt(-inf)=sNaN */
			return x*x + x;
		}
		
		/* take care of zero */
		if (x < 0.0) {
			return Double.NaN;
		} else if (x == 0.0) {
			return x;	/* sqrt(+-0) = +-0 */
		}
		
		/* normalize x */
		long m = (ix>>52);
		ix &= 0x000fffffffffffffL;

		/* add implicit bit, if not sub-normal */
		if (m != 0)  ix |= 0x0010000000000000L;
		
		m -= 1023L;	/* unbias exponent */
		if ((m&1) != 0) {	/* odd m, double x to make it even */
			ix += ix;
		}
		m >>= 1;	/* m = [m/2] */
		m += 1023L;

		/* generate sqrt(x) bit by bit */
		ix += ix;
		long q = 0L;	/* q = sqrt(x) */
		long s = 0L;
		long r = 0x0020000000000000L;	/* r = moving bit from right to left */

		while (r != 0) {
			long t = s + r; 
			if (t <= ix) { 
				s    = t + r; 
				ix  -= t; 
				q   += r;
			}
			ix += ix;
			r >>= 1;
		}

		/* round */
		if (ix != 0)  q += (q&1L);

		/* assemble result */
		ix = (m << 52) | (0x000fffffffffffffL&(q>>1));
		return Double.longBitsToDouble(ix);
	}

	

	static private final double halF[]	= {0.5, -0.5};
	static private final double twom1000 =
		Double.longBitsToDouble(0x0170000000000000L);  /* 2**-1000=9.33263618503218878990e-302 */

	static private final double o_threshold = Double.longBitsToDouble(0x40862e42fefa39efL);  /* 7.09782712893383973096e+02 */
	static private final double u_threshold = Double.longBitsToDouble(0xc0874910d52d3051L);  /* -7.45133219101941108420e+02 */
	static private final double ln2HI[] = {
		Double.longBitsToDouble(0x3fe62e42fee00000L),   /*  6.93147180369123816490e-01 */
		Double.longBitsToDouble(0xbfe62e42fee00000L)};  /* -6.93147180369123816490e-01 */
	static private final double ln2LO[] = {
		Double.longBitsToDouble(0x3dea39ef35793c76L),   /*  1.90821492927058770002e-10 */
		Double.longBitsToDouble(0xbdea39ef35793c76L)};  /* -1.90821492927058770002e-10 */
	static private final double invln2 = Double.longBitsToDouble(0x3ff71547652b82feL);  /* 1.44269504088896338700e+00 */
	static private final double P1 = Double.longBitsToDouble(0x3fc555555555553eL);  /*  1.66666666666666019037e-01 */
	static private final double P2 = Double.longBitsToDouble(0xbf66c16c16bebd93L);  /* -2.77777777770155933842e-03 */
	static private final double P3 = Double.longBitsToDouble(0x3f11566aaf25de2cL);  /*  6.61375632143793436117e-05 */
	static private final double P4 = Double.longBitsToDouble(0xbebbbd41c5d26bf1L);  /* -1.65339022054652515390e-06 */
	static private final double P5 = Double.longBitsToDouble(0x3e66376972bea4d0L);  /*  4.13813679705723846039e-08 */

	/* exp(x)
	 * Returns the exponential of x.
	 *
	 * Method
	 *   1. Argument reduction:
	 *      Reduce x to an r so that |r| <= 0.5*ln2 ~ 0.34658.
	 *	Given x, find r and integer k such that
	 *
	 *               x = k*ln2 + r,  |r| <= 0.5*ln2.  
	 *
	 *      Here r will be represented as r = hi-lo for better 
	 * 	accuracy.
	 *
	 *   2. Approximation of exp(r) by a special rational function on
	 *	the interval [0,0.34658]:
	 *	Write
	 *	    R(r**2) = r*(exp(r)+1)/(exp(r)-1) = 2 + r*r/6 - r**4/360 + ...
	 *      We use a special Reme algorithm on [0,0.34658] to generate 
	 * 	a polynomial of degree 5 to approximate R. The maximum error 
	 *  	of this polynomial approximation is bounded by 2**-59. In
	 *	other words,
	 *  	    R(z) ~ 2.0 + P1*z + P2*z**2 + P3*z**3 + P4*z**4 + P5*z**5
	 * 	(where z=r*r, and the values of P1 to P5 are listed below)
	 *	and
	 *	    |                  5          |     -59
	 * 	    | 2.0+P1*z+...+P5*z   -  R(z) | <= 2 
	 *	    |                             |
	 *	The computation of exp(r) thus becomes
	 *                             2*r
	 *		exp(r) = 1 + -------
	 *		              R - r
	 *                          r*R1(r)	
	 *		       = 1 + r + ----------- (for better accuracy)
	 *		                  2 - R1(r)
	 * 	where
	 *  			         2       4             10
	 *		R1(r) = r - (P1*r  + P2*r  + ... + P5*r   ).
	 *	
	 *   3. Scale back to obtain exp(x):
	 *	From step 1, we have
	 *	   exp(x) = 2^k * exp(r)
	 *
	 * Special cases:
	 *	exp(INF) is INF, exp(NaN) is NaN;
	 *	exp(-INF) is 0, and
	 *	for finite argument, only exp(0)=1 is exact.
	 *
	 * Accuracy:
	 *	according to an error analysis, the error is always less than
	 *	1 ulp (unit in the last place).
	 *
	 * Misc. info.
	 *	For IEEE double
	 *	    if x >  7.09782712893383973096e+02 then exp(x) overflow
	 *	    if x < -7.45133219101941108420e+02 then exp(x) underflow
	 */

	/**
	 *	Returns the exponential of its argument.
	 *	@param	x	The argument, a double.
	 *	@return	Returns e to the power x.
	 */
	static public double exp(double x)
	{
		double	y, hi=0, lo=0, c, t;
		int		k=0, xsb;
		int		hx;

		hx  = __HI(x);	/* high word of x */
		xsb = (hx>>>31)&1;		/* sign bit of x */
		hx &= 0x7fffffff;		/* high word of |x| */

		/* filter out non-finite argument */
		if (hx >= 0x40862E42) {			/* if |x|>=709.78... */
            if (hx>=0x7ff00000) {
				if (((hx&0xfffff)|__LO(x)) != 0) {
					return x+x; 		/* NaN */
				} else {
					return ((xsb==0) ? x : 0.0);	/* exp(+-inf)={inf,0} */
				}
			}
			if (x > o_threshold)
				return huge*huge; /* overflow */
			if (x < u_threshold)
				return twom1000*twom1000; /* underflow */
		}

		/* argument reduction */
		if (hx > 0x3fd62e42) {		/* if  |x| > 0.5 ln2 */ 
			if(hx < 0x3FF0A2B2) {	/* and |x| < 1.5 ln2 */
				hi = x-ln2HI[xsb]; lo=ln2LO[xsb]; k = 1-xsb-xsb;
			} else {
				k  = (int)(invln2*x+halF[xsb]);
				t  = k;
				hi = x - t*ln2HI[0];	/* t*ln2HI is exact here */
				lo = t*ln2LO[0];
			}
			x  = hi - lo;
		} else if(hx < 0x3e300000) {	/* when |x|<2**-28 */
			if (huge+x > one)
				return one+x;/* trigger inexact */
		} else {
			k = 0;
		}
		
		/* x is now in primary range */
		t  = x*x;
		c  = x - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
		if (k==0) {
			return one-((x*c)/(c-2.0)-x);
		} else {
			y = one-((lo-(x*c)/(2.0-c))-hi);
		}

		long iy = Double.doubleToLongBits(y);
		if (k >= -1021) {
			iy += ((long)k<<52);
		} else {
			iy += ((k+1000L)<<52);
		}
		return Double.longBitsToDouble(iy);
	}

	static private final double ln2_hi  = Double.longBitsToDouble(0x3fe62e42fee00000L);  /* 6.93147180369123816490e-01 */
	static private final double ln2_lo  = Double.longBitsToDouble(0x3dea39ef35793c76L);  /* 1.90821492927058770002e-10 */
	static private final double Lg1 = Double.longBitsToDouble(0x3fe5555555555593L);  /* 6.666666666666735130e-01 */
	static private final double Lg2 = Double.longBitsToDouble(0x3fd999999997fa04L);  /* 3.999999999940941908e-01 */
	static private final double Lg3 = Double.longBitsToDouble(0x3fd2492494229359L);  /* 2.857142874366239149e-01 */
	static private final double Lg4 = Double.longBitsToDouble(0x3fcc71c51d8e78afL);  /* 2.222219843214978396e-01 */
	static private final double Lg5 = Double.longBitsToDouble(0x3fc7466496cb03deL);  /* 1.818357216161805012e-01 */
	static private final double Lg6 = Double.longBitsToDouble(0x3fc39a09d078c69fL);  /* 1.531383769920937332e-01 */
	static private final double Lg7 = Double.longBitsToDouble(0x3fc2f112df3e5244L);  /* 1.479819860511658591e-01 */

	/*
	 * Return the logrithm of x
	 *
	 * Method :
	 *   1. Argument Reduction: find k and f such that 
	 *			x = 2^k * (1+f), 
	 *	   where  sqrt(2)/2 < 1+f < sqrt(2) .
	 *
	 *   2. Approximation of log(1+f).
	 *	Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s)
	 *		 = 2s + 2/3 s**3 + 2/5 s**5 + .....,
	 *	     	 = 2s + s*R
	 *      We use a special Reme algorithm on [0,0.1716] to generate 
	 * 	a polynomial of degree 14 to approximate R The maximum error 
	 *	of this polynomial approximation is bounded by 2**-58.45. In
	 *	other words,
	 *		        2      4      6      8      10      12      14
	 *	    R(z) ~ Lg1*s +Lg2*s +Lg3*s +Lg4*s +Lg5*s  +Lg6*s  +Lg7*s
	 *  	(the values of Lg1 to Lg7 are listed in the program)
	 *	and
	 *	    |      2          14          |     -58.45
	 *	    | Lg1*s +...+Lg7*s    -  R(z) | <= 2 
	 *	    |                             |
	 *	Note that 2s = f - s*f = f - hfsq + s*hfsq, where hfsq = f*f/2.
	 *	In order to guarantee error in log below 1ulp, we compute log
	 *	by
	 *		log(1+f) = f - s*(f - R)	(if f is not too large)
	 *		log(1+f) = f - (hfsq - s*(hfsq+R)).	(better accuracy)
	 *	
	 *	3. Finally,  log(x) = k*ln2 + log(1+f).  
	 *			    = k*ln2_hi+(f-(hfsq-(s*(hfsq+R)+k*ln2_lo)))
	 *	   Here ln2 is split into two floating point number: 
	 *			ln2_hi + ln2_lo,
	 *	   where n*ln2_hi is always exact for |n| < 2000.
	 *
	 * Special cases:
	 *	log(x) is NaN with signal if x < 0 (including -INF) ; 
	 *	log(+INF) is +INF; log(0) is -INF with signal;
	 *	log(NaN) is that NaN with no signal.
	 *
	 * Accuracy:
	 *	according to an error analysis, the error is always less than
	 *	1 ulp (unit in the last place).
	 */

	/**
	 *	Returns the natural logarithm of its argument.
	 *	@param	x	The argument, a double.
	 *	@return	Returns the natural (base e) logarithm of x.
	 */
	static public double log(double x)
	{
		double hfsq,f,s,z,R,w,t1,t2,dk;
		int k,hx,i,j;
		int lx;
		
		hx = __HI(x);		/* high word of x */
		lx = __LO(x);		/* low  word of x */

		k=0;
		if (hx < 0x00100000) {			/* x < 2**-1022  */
			if (((hx&0x7fffffff)|lx)==0) 
				return -two54/zero;		/* log(+-0)=-inf */
			if (hx<0)
				return (x-x)/zero;	/* log(-#) = NaN */
			k -= 54;
			x *= two54; /* subnormal number, scale up x */
			hx = __HI(x);		/* high word of x */
		} 
		if (hx >= 0x7ff00000)
			return x+x;
		k += (hx>>20)-1023;
		hx &= 0x000fffff;
		i = (hx+0x95f64)&0x100000;
		x = setHI(x, hx|(i^0x3ff00000));	/* normalize x or x/2 */
		k += (i>>20);
		f = x-1.0;
		if ((0x000fffff&(2+hx))<3) {	/* |f| < 2**-20 */
			if (f == zero) {
				if (k == 0) {
					return zero;
				} else {
					dk=(double)k;
				}
				return dk*ln2_hi+dk*ln2_lo;
			}
			R = f*f*(0.5-0.33333333333333333*f);
			if (k==0) {
				return f-R;
			} else {
				dk = (double)k;
				return dk*ln2_hi-((R-dk*ln2_lo)-f);
			}
		}
		s = f/(2.0+f); 
		dk = (double)k;
		z = s*s;
		i = hx-0x6147a;
		w = z*z;
		j = 0x6b851-hx;
		t1= w*(Lg2+w*(Lg4+w*Lg6)); 
		t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7))); 
		i |= j;
		R = t2+t1;
		if (i > 0) {
			hfsq = 0.5*f*f;
			if (k == 0) {
				return f-(hfsq-s*(hfsq+R));
			} else {
				return dk*ln2_hi-((hfsq-(s*(hfsq+R)+dk*ln2_lo))-f);
			}
		} else {
			if (k==0) {
				return f-s*(f-R);
			} else {
				return dk*ln2_hi-((s*(f-R)-dk*ln2_lo)-f);
			}
		}
	}


	/**
	 *	Returns the sine of its argument.
	 *	@param	x	The argument, a double, assumed to be in radians.
	 *	@return	Returns the sine of x.
	 */
	static public double sin(double x)
	{
		double	y[] = new double[2];
		double	z=0.0;
		int		n;
		int		ix = __HI(x);
		
		ix &= 0x7fffffff;	/* |x| ~< pi/4 */

		if (ix <= 0x3fe921fb) {
			return __kernel_sin(x,z,0);
		} else if (ix >= 0x7ff00000) {
			/* sin(Inf or NaN) is NaN */
			return x-x;
		} else {
			/* argument reduction needed */	
			n = __ieee754_rem_pio2(x, y);
			switch(n&3) {
			case 0:
				return  __kernel_sin(y[0],y[1], 1);
			case 1:
				return  __kernel_cos(y[0],y[1]);
			case 2:
				return -__kernel_sin(y[0],y[1], 1);
			default:
				return -__kernel_cos(y[0],y[1]);
			}
		}
	}


	static private double S1  = -1.66666666666666324348e-01; /* 0xBFC55555, 0x55555549 */
	static private double S2  =  8.33333333332248946124e-03; /* 0x3F811111, 0x1110F8A6 */
	static private double S3  = -1.98412698298579493134e-04; /* 0xBF2A01A0, 0x19C161D5 */
	static private double S4  =  2.75573137070700676789e-06; /* 0x3EC71DE3, 0x57B1FE7D */
	static private double S5  = -2.50507602534068634195e-08; /* 0xBE5AE5E6, 0x8A2B9CEB */
	static private double S6  =  1.58969099521155010221e-10; /* 0x3DE5D93A, 0x5ACFD57C */
															 
	/*
	 * kernel sin function on [-pi/4, pi/4], pi/4 ~ 0.7854
	 * Input x is assumed to be bounded by ~pi/4 in magnitude.
	 * Input y is the tail of x. * Input iy indicates whether y is 0. (if iy=0, y assume to be 0). 
	 *
	 * Algorithm
	 *	1. Since sin(-x) = -sin(x), we need only to consider positive x. 
	 *	2. if x < 2^-27 (hx<0x3e400000 0), return x with inexact if x!=0.
	 *	3. sin(x) is approximated by a polynomial of degree 13 on
	 *	   [0,pi/4]
	 *		  	         3            13
	 *	   	sin(x) ~ x + S1*x + ... + S6*x
	 *	   where
	 *	
	 * 	|sin(x)         2     4     6     8     10     12  |     -58
	 * 	|----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x  +S6*x   )| <= 2
	 * 	|  x 					           | 
	 * 
	 *	4. sin(x+y) = sin(x) + sin'(x')*y
	 *		    ~ sin(x) + (1-x*x/2)*y
	 *	   For better accuracy, let 
	 *		     3      2      2      2      2
	 *		r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6))))
	 *	   then                   3    2
	 *		sin(x) = x + (S1*x + (x *(r-y/2)+y))
	 */
	static double __kernel_sin(double x, double y, int iy)
	{
		double z,r,v;
		int ix;
		ix = __HI(x)&0x7fffffff;	/* high word of x */
		if (ix<0x3e400000) {			/* |x| < 2**-27 */
			if((int)x ==0 )
				return x;		/* generate inexact */
		}
		z	=  x*x;
		v	=  z*x;
		r	=  S2+z*(S3+z*(S4+z*(S5+z*S6)));
		if (iy == 0)
			return x+v*(S1+z*r);
		else
			return x-((z*(half*y-v*r)-y)-v*S1);
	}

	/**
	 *	Returns the cosine of its argument.
	 *	@param	x	The argument, a double, assumed to be in radians.
	 *	@return	Returns the cosine of x.
	 */
	static public double cos(double x)
	{
		double z = 0.0;
		double y[] = new double[2];
		int n, ix;
		
		/* High word of x. */
		ix = __HI(x);
		
		/* |x| ~< pi/4 */
		ix &= 0x7fffffff;
		if (ix <= 0x3fe921fb) {
			return __kernel_cos(x,z);
		
		/* cos(Inf or NaN) is NaN */
		} else if (ix >= 0x7ff00000) {
			return x-x;
		
		/* argument reduction needed */
		} else {
			n = __ieee754_rem_pio2(x,y);
			switch(n&3) {
			case 0: return  __kernel_cos(y[0],y[1]);
			case 1: return -__kernel_sin(y[0],y[1],1);
			case 2: return -__kernel_cos(y[0],y[1]);
			default:
				return  __kernel_sin(y[0],y[1],1);
			}
		}
	}

	static private final double one = Double.longBitsToDouble(0x3ff0000000000000L);  /*  1.00000000000000000000e+00 */
	static private final double C1  = Double.longBitsToDouble(0x3fa555555555554cL);  /*  4.16666666666666019037e-02 */
	static private final double C2  = Double.longBitsToDouble(0xbf56c16c16c15177L);  /* -1.38888888888741095749e-03 */
	static private final double C3  = Double.longBitsToDouble(0x3efa01a019cb1590L);  /*  2.48015872894767294178e-05 */
	static private final double C4  = Double.longBitsToDouble(0xbe927e4f809c52adL);  /* -2.75573143513906633035e-07 */
	static private final double C5  = Double.longBitsToDouble(0x3e21ee9ebdb4b1c4L);  /*  2.08757232129817482790e-09 */
	static private final double C6  = Double.longBitsToDouble(0xbda8fae9be8838d4L);  /* -1.13596475577881948265e-11 */

	/*
	 * kernel cos function on [-pi/4, pi/4], pi/4 ~ 0.785398164
	 * Input x is assumed to be bounded by ~pi/4 in magnitude.
	 * Input y is the tail of x. 
	 *
	 * Algorithm
	 *	1. Since cos(-x) = cos(x), we need only to consider positive x.
	 *	2. if x < 2^-27 (hx<0x3e400000 0), return 1 with inexact if x!=0.
	 *	3. cos(x) is approximated by a polynomial of degree 14 on
	 *	   [0,pi/4]
	 *                               4            14
	 *	   	cos(x) ~ 1 - x*x/2 + C1*x + ... + C6*x
	 *	   where the remez error is
	 *	
	 * 	|              2     4     6     8     10    12     14 |     -58
	 * 	|cos(x)-(1-.5*x +C1*x +C2*x +C3*x +C4*x +C5*x  +C6*x  )| <= 2
	 * 	|    					               | 
	 * 
	 * 	               4     6     8     10    12     14 
	 *	4. let r = C1*x +C2*x +C3*x +C4*x +C5*x  +C6*x  , then
	 *	       cos(x) = 1 - x*x/2 + r
	 *	   since cos(x+y) ~ cos(x) - sin(x)*y 
	 *			  ~ cos(x) - x*y,
	 *	   a correction term is necessary in cos(x) and hence
	 *		cos(x+y) = 1 - (x*x/2 - (r - x*y))
	 *	   For better accuracy when x > 0.3, let qx = |x|/4 with
	 *	   the last 32 bits mask off, and if x > 0.78125, let qx = 0.28125.
	 *	   Then
	 *		cos(x+y) = (1-qx) - ((x*x/2-qx) - (r-x*y)).
	 *	   Note that 1-qx and (x*x/2-qx) is EXACT here, and the
	 *	   magnitude of the latter is at least a quarter of x*x/2,
	 *	   thus, reducing the rounding error in the subtraction.
	 */
	static private double __kernel_cos(double x, double y)
	{
		double	a, hz, z, r, qx=zero;
		int		ix;
		ix = __HI(x)&0x7fffffff;	/* ix = |x|'s high word*/
		if (ix < 0x3e400000) {
			/* if x < 2**27 */
			if (((int)x) == 0) return one;		/* generate inexact */
		}
		z  = x*x;
		r  = z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*C6)))));
		if (ix < 0x3FD33333) {
			/* if |x| < 0.3 */ 
			return one - (0.5*z - (z*r - x*y));
		} else {
			if(ix > 0x3fe90000) {		/* x > 0.78125 */
				qx = 0.28125;
			} else {
				qx = set(ix-0x00200000, 0);/* x/4 */
			}
			hz = 0.5*z-qx;
			a  = one-qx;
			return a - (hz - (z*r-x*y));
		}
	}

	/**
	 *	Returns the tangent of its argument.
	 *	@param	x	The argument, a double, assumed to be in radians.
	 *	@return	Returns the tangent of x.
	 */	
	static public double tan(double x)
	{
		double	z = zero;
		
		int		n;
		int		ix = __HI(x);
		
		/* |x| ~< pi/4 */
		ix &= 0x7fffffff;
		if (ix <= 0x3fe921fb) {
			return __kernel_tan(x, z, 1);
		} else if (ix >= 0x7ff00000) {
			/* tan(Inf or NaN) is NaN */
			return x-x;		/* NaN */
		} else {
			/* argument reduction needed */
			double	y[] = new double[2];
			n = __ieee754_rem_pio2(x, y);
			/*   1 -- n even -1 -- n odd */
			return __kernel_tan(y[0], y[1], 1-((n&1)<<1));
		}
	}


	static private final double pio4  = Double.longBitsToDouble(0x3fe921fb54442d18L);  /* 7.85398163397448278999e-01 */
	static private final double pio4lo= Double.longBitsToDouble(0x3c81a62633145c07L);  /* 3.06161699786838301793e-17 */
	static private final double T[] =  {
		Double.longBitsToDouble(0x3fd5555555555563L),  /* 3.33333333333334091986e-01 */
		Double.longBitsToDouble(0x3fc111111110fe7aL),  /* 1.33333333333201242699e-01 */
		Double.longBitsToDouble(0x3faba1ba1bb341feL),  /* 5.39682539762260521377e-02 */
		Double.longBitsToDouble(0x3f9664f48406d637L),  /* 2.18694882948595424599e-02 */
		Double.longBitsToDouble(0x3f8226e3e96e8493L),  /* 8.86323982359930005737e-03 */
		Double.longBitsToDouble(0x3f6d6d22c9560328L),  /* 3.59207910759131235356e-03 */
		Double.longBitsToDouble(0x3f57dbc8fee08315L),  /* 1.45620945432529025516e-03 */
		Double.longBitsToDouble(0x3f4344d8f2f26501L),  /* 5.88041240820264096874e-04 */
		Double.longBitsToDouble(0x3f3026f71a8d1068L),  /* 2.46463134818469906812e-04 */
		Double.longBitsToDouble(0x3f147e88a03792a6L),  /* 7.81794442939557092300e-05 */
		Double.longBitsToDouble(0x3f12b80f32f0a7e9L),  /* 7.14072491382608190305e-05 */
		Double.longBitsToDouble(0xbef375cbdb605373L),  /* -1.85586374855275456654e-05 */
		Double.longBitsToDouble(0x3efb2a7074bf7ad4L)   /* 2.59073051863633712884e-05 */
	};
	
	/*
	 *	__kernel_tan( x, y, k )
	 * kernel tan function on [-pi/4, pi/4], pi/4 ~ 0.7854
	 * Input x is assumed to be bounded by ~pi/4 in magnitude.
	 * Input y is the tail of x. * Input k indicates whether tan (if k=1) or 
	 * -1/tan (if k= -1) is returned. * * Algorithm
	 *	1. Since tan(-x) = -tan(x), we need only to consider positive x. 
	 *	2. if x < 2^-28 (hx<0x3e300000 0), return x with inexact if x!=0.
	 *	3. tan(x) is approximated by a odd polynomial of degree 27 on
	 *	   [0,0.67434]
	 *                       3             27
	 *	   	tan(x) ~ x + T1*x + ... + T13*x
	 *	   where
	 *	
	 * 	        |tan(x)         2     4            26   |     -59.2
	 * 	        |----- - (1+T1*x +T2*x +.... +T13*x    )| <= 2
	 *          |  x                                    |
	 *
	 *	   Note: tan(x+y) = tan(x) + tan'(x)*y
	 *		          ~ tan(x) + (1+x*x)*y
	 *	   Therefore, for better accuracy in computing tan(x+y), let 
	 *		     3      2      2       2       2
	 *		r = x *(T2+x *(T3+x *(...+x *(T12+x *T13))))
	 *	   then
	 *		 		    3    2
	 *		tan(x+y) = x + (T1*x + (x *(r+y)+y)) *
	 *   4. For x in [0.67434,pi/4],  let y = pi/4 - x, then
	 *		tan(x) = tan(pi/4-y) = (1-tan(y))/(1+tan(y))
	 *		       = 1 - 2*(tan(y) - (tan(y)^2)/(1+tan(y)))
	 */
	static private double __kernel_tan(double x, double y, int iy)
	{
		double z, r, v, w, s;
		int	ix,hx;
		
		hx = __HI(x);	/* high word of x */
		ix = hx&0x7fffffff;	/* high word of |x| */
		if (ix<0x3e300000) {			/* x < 2**-28 */
			if ((int)x==0) {			/* generate inexact */
				if(((ix|__LO(x))|(iy+1))==0)
					return one/abs(x);
				else return (iy==1)? x: -one/x;
			}
		}
		if (ix>=0x3FE59428) {
			/* |x|>=0.6744 */
			if (hx<0) {
				x = -x;
				y = -y;
			}
			z = pio4-x;
			w = pio4lo-y;
			x = z+w;
			y = 0.0;
		}
		z	=  x*x;
		w 	=  z*z;
		
		/*
		 *	Break x^5*(T[1]+x^2*T[2]+...) into
		 *	  x^5(T[1]+x^4*T[3]+...+x^20*T[11]) + 
		 *	  x^5(x^2*(T[2]+x^4*T[4]+...+x^22*[T12]))
		 */
		r = T[1]+w*(T[3]+w*(T[5]+w*(T[7]+w*(T[9]+w*T[11]))));
		v = z*(T[2]+w*(T[4]+w*(T[6]+w*(T[8]+w*(T[10]+w*T[12])))));
		s = z*x;
		r = y + z*(s*(r+v)+y);
		r += T[0]*s;
		w = x+r;
		if (ix >= 0x3FE59428) {
			v = (double)iy;
			return (double)(1-((hx>>30)&2))*(v-2.0*(x-(w*w/(w+v)-r)));
		}
		if (iy==1) {
			return w;
		} else {
			/* if allow error up to 2 ulp, simply return -1.0/(x+r) here */
			/*  compute -1.0/(x+r) accurately */
			double a,t;
			z  = w;
			z = setLO(z, 0);
			v  = r-(z - x);
			/* z+v = r+x */
			t = a  = -1.0/w;
			/* a = -1.0/w */
			t = setLO(t, 0);
			s  = 1.0+t*z;
			return t+a*(s+t*v);
		}
	}


	static private final double pio2_hi = Double.longBitsToDouble(0x3FF921FB54442D18L);  /* 1.57079632679489655800e+00 */
	static private final double pio2_lo = Double.longBitsToDouble(0x3C91A62633145C07L);  /* 6.12323399573676603587e-17 */
	static private final double pio4_hi = Double.longBitsToDouble(0x3FE921FB54442D18L);  /* 7.85398163397448278999e-01 */
	/* coefficient for R(x^2) */
	static private final double pS0 = Double.longBitsToDouble(0x3fc5555555555555L);  /*  1.66666666666666657415e-01 */
	static private final double pS1 = Double.longBitsToDouble(0xbfd4d61203eb6f7dL);  /* -3.25565818622400915405e-01 */
	static private final double pS2 = Double.longBitsToDouble(0x3fc9c1550e884455L);  /*  2.01212532134862925881e-01 */
	static private final double pS3 = Double.longBitsToDouble(0xbfa48228b5688f3bL);  /* -4.00555345006794114027e-02 */
	static private final double pS4 = Double.longBitsToDouble(0x3f49efe07501b288L);  /*  7.91534994289814532176e-04 */
	static private final double pS5 = Double.longBitsToDouble(0x3f023de10dfdf709L);  /*  3.47933107596021167570e-05 */
	static private final double qS1 = Double.longBitsToDouble(0xc0033a271c8a2d4bL);  /* -2.40339491173441421878e+00 */
	static private final double qS2 = Double.longBitsToDouble(0x40002ae59c598ac8L);  /*  2.02094576023350569471e+00 */
	static private final double qS3 = Double.longBitsToDouble(0xbfe6066c1b8d0159L);  /* -6.88283971605453293030e-01 */
	static private final double qS4 = Double.longBitsToDouble(0x3fb3b8c5b12e9282L);  /*  7.70381505559019352791e-02 */

	/*
	 *	asin(x)
	 * Method :
	 *	Since  asin(x) = x + x^3/6 + x^5*3/40 + x^7*15/336 + ...
	 *	we approximate asin(x) on [0,0.5] by
	 *		asin(x) = x + x*x^2*R(x^2)
	 *	where
	 *		R(x^2) is a rational approximation of (asin(x)-x)/x^3 
	 *	and its remez error is bounded by
	 *		|(asin(x)-x)/x^3 - R(x^2)| < 2^(-58.75)
	 *
	 *	For x in [0.5,1]
	 *		asin(x) = pi/2-2*asin(sqrt((1-x)/2))
	 *	Let y = (1-x), z = y/2, s := sqrt(z), and pio2_hi+pio2_lo=pi/2;
	 *	then for x>0.98
	 *		asin(x) = pi/2 - 2*(s+s*z*R(z))
	 *			= pio2_hi - (2*(s+s*z*R(z)) - pio2_lo)
	 *	For x<=0.98, let pio4_hi = pio2_hi/2, then
	 *		f = hi part of s;
	 *		c = sqrt(z) - f = (z-f*f)/(s+f) 	...f+c=sqrt(z)
	 *	and
	 *		asin(x) = pi/2 - 2*(s+s*z*R(z))
	 *			= pio4_hi+(pio4-2s)-(2s*z*R(z)-pio2_lo)
	 *			= pio4_hi+(pio4-2f)-(2s*z*R(z)-(pio2_lo+2c))
	 *
	 * Special cases:
	 *	if x is NaN, return x itself;
	 *	if |x|>1, return NaN with invalid signal.
	 *
	 */

	/**
	 *	Returns the inverse (arc) sine of its argument.
	 *	@param	x	The argument, a double.
	 *	@return	Returns the angle, in radians, whose sine is x.
	 *			It is in the range [-pi/2,pi/2].
	 */
	static public double asin(double x)
	{
		double t=zero,w,p,q,c,r,s;
		int hx,ix;
		hx = __HI(x);
		
		ix = hx&0x7fffffff;
		if (ix>= 0x3ff00000) {		/* |x|>= 1 */
			if(((ix-0x3ff00000)|__LO(x))==0)
				/* asin(1)=+-pi/2 with inexact */
				return x*pio2_hi+x*pio2_lo;	
			return (x-x)/(x-x);		/* asin(|x|>1) is NaN */   
		} else if (ix<0x3fe00000) {	/* |x|<0.5 */
			if (ix<0x3e400000) {		/* if |x| < 2**-27 */
				if(huge+x>one) return x;/* return x with inexact if x!=0*/
			} else 
				t = x*x;
			p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5)))));
			q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4)));
			w = p/q;
			return x+x*w;
		}
		/* 1> |x|>= 0.5 */
		w = one - abs(x);
		t = w*0.5;
		p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5)))));
		q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4)));
		s = sqrt(t);
		if(ix>=0x3FEF3333) { 	/* if |x| > 0.975 */
			w = p/q;
			t = pio2_hi-(2.0*(s+s*w)-pio2_lo);
		} else {
			w  = s;
			w  = setLO(w, 0);
			c  = (t-w*w)/(s+w);
			r  = p/q;
			p  = 2.0*s*r-(pio2_lo-2.0*c);
			q  = pio4_hi-2.0*w;
			t  = pio4_hi-(p-q);
		}    
		return ((hx>0) ? t : -t);
	}

	/*
	 * Method :
	 *	acos(x)  = pi/2 - asin(x)
	 *	acos(-x) = pi/2 + asin(x)
	 * For |x|<=0.5
	 *	acos(x) = pi/2 - (x + x*x^2*R(x^2))	(see asin.c)
	 * For x>0.5
	 * 	acos(x) = pi/2 - (pi/2 - 2asin(sqrt((1-x)/2)))
	 *		= 2asin(sqrt((1-x)/2))  
	 *		= 2s + 2s*z*R(z) 	...z=(1-x)/2, s=sqrt(z)
	 *		= 2f + (2c + 2s*z*R(z))
	 *     where f=hi part of s, and c = (z-f*f)/(s+f) is the correction term
	 *     for f so that f+c ~ sqrt(z).
	 * For x<-0.5
	 *	acos(x) = pi - 2asin(sqrt((1-|x|)/2))
	 *          = pi - 0.5*(s+s*z*R(z)), where z=(1-|x|)/2,s=sqrt(z)
	 *
	 * Special cases:
	 *	if x is NaN, return x itself;
	 *	if |x|>1, return NaN with invalid signal.
	 *
	 * Function needed: sqrt
	 */

	/**
	 *	Returns the inverse (arc) cosine of its argument.
	 *	@param	x	The argument, a double.
	 *	@return	Returns the angle, in radians, whose cosine is x.
	 *			It is in the range [0,pi].
	 */
	static public double acos(double x)
	{
		double z,p,q,r,w,s,c,df;
		int hx,ix;
		hx = __HI(x);
		ix = hx&0x7fffffff;
		if (ix >= 0x3ff00000) {	/* |x| >= 1 */
			if (((ix-0x3ff00000)|__LO(x)) == 0) {	/* |x|==1 */
				if (hx>0) 
					return 0.0;		/* acos(1) = 0  */
				else
					return PI+2.0*pio2_lo;	/* acos(-1)= pi */
			}
			return (x-x)/(x-x);		/* acos(|x|>1) is NaN */
		}
		if (ix < 0x3fe00000) {	/* |x| < 0.5 */
			if (ix <= 0x3c600000)
				return pio2_hi+pio2_lo;/*if|x|<2**-57*/
			z = x*x;
			p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
			q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
			r = p/q;
			return pio2_hi - (x - (pio2_lo-x*r));
		} else if (hx<0) {		/* x < -0.5 */
			z = (one+x)*0.5;
			p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
			q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
			s = sqrt(z);
			r = p/q;
			w = r*s-pio2_lo;
			return PI - 2.0*(s+w);
		} else {			/* x > 0.5 */
			z = (one-x)*0.5;
			s = sqrt(z);
			df = s;
			df = setLO(df, 0);
			c  = (z-df*df)/(s+df);
			p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
			q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
			r = p/q;
			w = r*s+c;
			return 2.0*(df+w);
		}
	}


	static private final double atanhi[] = {
		Double.longBitsToDouble(0x3fddac670561bb4fL),  /* 4.63647609000806093515e-01 atan(0.5)hi  */
		Double.longBitsToDouble(0x3fe921fb54442d18L),  /* 7.85398163397448278999e-01 atan(1.0)hi  */
		Double.longBitsToDouble(0x3fef730bd281f69bL),  /* 9.82793723247329054082e-01 atan(1.5)hi  */
		Double.longBitsToDouble(0x3ff921fb54442d18L)   /* 1.57079632679489655800e+00 atan(inf)hi  */
	};

	static private final double atanlo[] = {
		Double.longBitsToDouble(0x3c7a2b7f222f65e2L),  /* 2.26987774529616870924e-17 atan(0.5)lo  */
		Double.longBitsToDouble(0x3c81a62633145c07L),  /* 3.06161699786838301793e-17 atan(1.0)lo  */
		Double.longBitsToDouble(0x3c7007887af0cbbdL),  /* 1.39033110312309984516e-17 atan(1.5)lo  */
		Double.longBitsToDouble(0x3c91a62633145c07L)   /* 6.12323399573676603587e-17 atan(inf)lo  */
	};

	static private final double aT[] = {
		Double.longBitsToDouble(0x3fd555555555550dL),  /*  3.33333333333329318027e-01 */
		Double.longBitsToDouble(0xbfc999999998ebc4L),  /* -1.99999999998764832476e-01 */
		Double.longBitsToDouble(0x3fc24924920083ffL),  /*  1.42857142725034663711e-01 */
		Double.longBitsToDouble(0xbfbc71c6fe231671L),  /* -1.11111104054623557880e-01 */
		Double.longBitsToDouble(0x3fb745cdc54c206eL),  /*  9.09088713343650656196e-02 */
		Double.longBitsToDouble(0xbfb3b0f2af749a6dL),  /* -7.69187620504482999495e-02 */
		Double.longBitsToDouble(0x3fb10d66a0d03d51L),  /*  6.66107313738753120669e-02 */
		Double.longBitsToDouble(0xbfadde2d52defd9aL),  /* -5.83357013379057348645e-02 */
		Double.longBitsToDouble(0x3fa97b4b24760debL),  /*  4.97687799461593236017e-02 */
		Double.longBitsToDouble(0xbfa2b4442c6a6c2fL),  /* -3.65315727442169155270e-02 */
		Double.longBitsToDouble(0x3f90ad3ae322da11L)   /*  1.62858201153657823623e-02 */
	};

	/*
	 * Method
	 *   1. Reduce x to positive by atan(x) = -atan(-x).
	 *   2. According to the integer k=4t+0.25 chopped, t=x, the argument
	 *      is further reduced to one of the following intervals and the
	 *      arctangent of t is evaluated by the corresponding formula:
	 *
	 *      [0,7/16]      atan(x) = t-t^3*(a1+t^2*(a2+...(a10+t^2*a11)...)
	 *      [7/16,11/16]  atan(x) = atan(1/2) + atan( (t-0.5)/(1+t/2) )
	 *      [11/16.19/16] atan(x) = atan( 1 ) + atan( (t-1)/(1+t) )
	 *      [19/16,39/16] atan(x) = atan(3/2) + atan( (t-1.5)/(1+1.5t) )
	 *      [39/16,INF]   atan(x) = atan(INF) + atan( -1/t )
	 *
	 * Constants:
	 * The hexadecimal values are the intended ones for the following 
	 * constants. The decimal values may be used, provided that the 
	 * compiler will convert from decimal to binary accurately enough 
	 * to produce the hexadecimal values shown.
	 */

	/**
	 *	Returns the inverse (arc) tangent of its argument.
	 *	@param	x	The argument, a double.
	 *	@return	Returns the angle, in radians, whose tangent is x.
	 *			It is in the range [-pi/2,pi/2].
	 */
	static public double atan(double x)
	{
		double w,s1,s2,z;
		int ix,hx,id;

		hx = __HI(x);
		ix = hx&0x7fffffff;
		if(ix>=0x44100000) {	/* if |x| >= 2^66 */
			if(ix>0x7ff00000||
				(ix==0x7ff00000&&(__LO(x)!=0)))
				return x+x;		/* NaN */
			if(hx>0) return  atanhi[3]+atanlo[3];
			else     return -atanhi[3]-atanlo[3];
		} if (ix < 0x3fdc0000) {	/* |x| < 0.4375 */
			if (ix < 0x3e200000) {	/* |x| < 2^-29 */
				if(huge+x>one) return x;	/* raise inexact */
			}
			id = -1;
		} else {
			x = abs(x);
			if (ix < 0x3ff30000) {		/* |x| < 1.1875 */
				if (ix < 0x3fe60000) {	/* 7/16 <=|x|<11/16 */
					id = 0; x = (2.0*x-one)/(2.0+x); 
				} else {			/* 11/16<=|x|< 19/16 */
					id = 1; x  = (x-one)/(x+one); 
				}
			} else {
				if (ix < 0x40038000) {	/* |x| < 2.4375 */
					id = 2; x  = (x-1.5)/(one+1.5*x);
				} else {			/* 2.4375 <= |x| < 2^66 */
					id = 3; x  = -1.0/x;
				}
			}
		}
		/* end of argument reduction */
		z = x*x;
		w = z*z;
		/* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */
		s1 = z*(aT[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10])))));
		s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9]))));
		if (id<0) return x - x*(s1+s2);
		else {
			z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);
			return (hx<0)? -z:z;
		}
	}


	static private final double pi_o_4 = Double.longBitsToDouble(0x3fe921fb54442d18L);  /* 7.8539816339744827900e-01 */
	static private final double pi_o_2 = Double.longBitsToDouble(0x3ff921fb54442d18L);  /* 1.5707963267948965580e+00 */
	static private final double pi_lo  = Double.longBitsToDouble(0x3ca1a62633145c07L);  /* 1.2246467991473531772e-16 */

	/*
	* Method :
	*	1. Reduce y to positive by atan2(y,x)=-atan2(-y,x).
	*	2. Reduce x to positive by (if x and y are unexceptional): 
	*		ARG (x+iy) = arctan(y/x)   	   ... if x > 0,
	*		ARG (x+iy) = pi - arctan[y/(-x)]   ... if x < 0,
	*
	* Special cases:
	*
	*	ATAN2((anything), NaN ) is NaN;
	*	ATAN2(NAN , (anything) ) is NaN;
	*	ATAN2(+-0, +(anything but NaN)) is +-0  ;
	*	ATAN2(+-0, -(anything but NaN)) is +-pi ;
	*	ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2;
	*	ATAN2(+-(anything but INF and NaN), +INF) is +-0 ;
	*	ATAN2(+-(anything but INF and NaN), -INF) is +-pi;
	*	ATAN2(+-INF,+INF ) is +-pi/4 ;
	*	ATAN2(+-INF,-INF ) is +-3pi/4;
	*	ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2;
	*
	* Constants:
	* The hexadecimal values are the intended ones for the following 
	* constants. The decimal values may be used, provided that the 
	* compiler will convert from decimal to binary accurately enough 
	* to produce the hexadecimal values shown.
	*/

	/**
	 *	Returns angle corresponding to a Cartesian point.
	 *	@param	x	The first argument, a double.
	 *	@param	y	The second argument, a double.
	 *	@return	Returns the angle, in radians, the the line
	 *			from (0,0) to (x,y) makes with the x-axis.
	 *			It is in the range [-pi,pi].
	 */
	static public double atan2(double y, double x)
	{  
		double z;
		int k,m,hx,hy,ix,iy;
		int lx,ly;
		
		hx = __HI(x);
		ix = hx&0x7fffffff;
		lx = __LO(x);
		hy = __HI(y);
		iy = hy&0x7fffffff;
		ly = __LO(y);
		if (((ix|((lx|-lx)>>>31))>0x7ff00000)||
			((iy|((ly|-ly)>>>31))>0x7ff00000))	/* x or y is NaN */
			return x+y;
		if ((hx-0x3ff00000|lx) == 0)
			return atan(y);   /* x=1.0 */
		m = ((hy>>31)&1)|((hx>>30)&2);	/* 2*sign(x)+sign(y) */

		/* when y = 0 */
		if((iy|ly)==0) {
			switch(m) {
			case 0: 
			case 1: return y; 	/* atan(+-0,+anything)=+-0 */
			case 2: return  PI+tiny;/* atan(+0,-anything) = pi */
			case 3: return -PI-tiny;/* atan(-0,-anything) =-pi */
			}
		}
		/* when x = 0 */
		if((ix|lx) == 0)
			return ((hy<0) ? -pi_o_2-tiny: pi_o_2+tiny);
	    
		/* when x is INF */
		if (ix == 0x7ff00000) {
			if (iy == 0x7ff00000) {
				switch(m) {
				case 0: return  pi_o_4+tiny;/* atan(+INF,+INF) */
				case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */
				case 2: return  3.0*pi_o_4+tiny;/*atan(+INF,-INF)*/
				case 3: return -3.0*pi_o_4-tiny;/*atan(-INF,-INF)*/
				}
			} else {
				switch(m) {
				case 0: return  zero  ;	/* atan(+...,+INF) */
				case 1: return -zero  ;	/* atan(-...,+INF) */
				case 2: return  PI+tiny  ;	/* atan(+...,-INF) */
				case 3: return -PI-tiny  ;	/* atan(-...,-INF) */
				}
			}
		}
		/* when y is INF */
		if(iy==0x7ff00000) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;

		/* compute y/x */
		k = (iy-ix)>>20;
		if (k > 60) {
			/* |y/x| >  2**60 */
			z=pi_o_2+0.5*pi_lo;
		} else if (hx<0&&k<-60) {
			/* |y|/x < -2**60 */
			z=0.0;
		} else {
			/* safe to do y/x */
			z=atan(abs(y/x));
		}

		switch (m) {
		case 0:
			return z  ;	/* atan(+,+) */
		case 1:
			return setHI(z, __HI(z) ^ 0x80000000);	/* atan(-,+) */
		case 2:
			return PI-(z-pi_lo);/* atan(+,-) */
		default: /* case 3 */
			return  (z-pi_lo)-PI;/* atan(-,-) */
		}
	}



	/*
	 * kernel function:
	 *	__kernel_sin		... sine function on [-pi/4,pi/4]
	 *	__ieee754_rem_pio2	... argument reduction routine
	 *
	 * Method.
	 *      Let S,C and T denote the sin, cos and tan respectively on 
	 *	[-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2 
	 *	in [-pi/4 , +pi/4], and let n = k mod 4.
	 *	We have
	 *
	 *          n        sin(x)      cos(x)        tan(x)
	 *     ----------------------------------------------------------
	 *	    0	       S	   C		 T
	 *	    1	       C	  -S		-1/T
	 *	    2	      -S	  -C		 T
	 *	    3	      -C	   S		-1/T
	 *     ----------------------------------------------------------
	 *
	 * Special cases:
	 *      Let trig be any of sin, cos, or tan.
	 *      trig(+-INF)  is NaN, with signals;
	 *      trig(NaN)    is that NaN;
	 *
	 * Accuracy:
	 *	TRIG(x) returns trig(x) nearly rounded 
	 */



	/*
	 * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi 
	 */
	static private final int two_over_pi[] = {
		0xa2f983, 0x6e4e44, 0x1529fc, 0x2757d1, 0xf534dd, 0xc0db62, 
		0x95993c, 0x439041, 0xfe5163, 0xabdebb, 0xc561b7, 0x246e3a, 
		0x424dd2, 0xe00649, 0x2eea09, 0xd1921c, 0xfe1deb, 0x1cb129, 
		0xa73ee8, 0x8235f5, 0x2ebb44, 0x84e99c, 0x7026b4, 0x5f7e41, 
		0x3991d6, 0x398353, 0x39f49c, 0x845f8b, 0xbdf928, 0x3b1ff8, 
		0x97ffde, 0x05980f, 0xef2f11, 0x8b5a0a, 0x6d1f6d, 0x367ecf, 
		0x27cb09, 0xb74f46, 0x3f669e, 0x5fea2d, 0x7527ba, 0xc7ebe5, 
		0xf17b3d, 0x0739f7, 0x8a5292, 0xea6bfb, 0x5fb11f, 0x8d5d08, 
		0x560330, 0x46fc7b, 0x6babf0, 0xcfbc20, 0x9af436, 0x1da9e3, 
		0x91615e, 0xe61b08, 0x659985, 0x5f14a0, 0x68408d, 0xffd880, 
		0x4d7327, 0x310606, 0x1556ca, 0x73a8c9, 0x60e27b, 0xc08c6b};

	static private final int  npio2_hw[] = {
		0x3ff921fb, 0x400921fb, 0x4012d97c, 0x401921fb, 0x401f6a7a, 0x4022d97c,
		0x4025fdbb, 0x402921fb, 0x402c463a, 0x402f6a7a, 0x4031475c, 0x4032d97c,
		0x40346b9c, 0x4035fdbb, 0x40378fdb, 0x403921fb, 0x403ab41b, 0x403c463a,
		0x403dd85a, 0x403f6a7a, 0x40407e4c, 0x4041475c, 0x4042106c, 0x4042d97c,
		0x4043a28c, 0x40446b9c, 0x404534ac, 0x4045fdbb, 0x4046c6cb, 0x40478fdb,
		0x404858eb, 0x404921fb};

	static private final double zero =  0.00000000000000000000e+00;	 // 0x0000000000000000 
	static private final double half =    Double.longBitsToDouble(0x3fe0000000000000L);  /* 5.00000000000000000000e-01 */
	static private final double two24 =   Double.longBitsToDouble(0x4170000000000000L);  /* 1.67772160000000000000e+07 */
	static private final double invpio2 = Double.longBitsToDouble(0x3fe45f306dc9c883L);  /* 6.36619772367581382433e-01 53 bits of 2/pi */
	static private final double pio2_1  = Double.longBitsToDouble(0x3ff921fb54400000L);  /* 1.57079632673412561417e+00 first  33 bit of pi/2 */
	static private final double pio2_1t = Double.longBitsToDouble(0x3dd0b4611a626331L);  /* 6.07710050650619224932e-11 pi/2 - pio2_1 */
	static private final double pio2_2  = Double.longBitsToDouble(0x3dd0b4611a600000L);  /* 6.07710050630396597660e-11 second 33 bit of pi/2 */
	static private final double pio2_2t = Double.longBitsToDouble(0x3ba3198a2e037073L);  /* 2.02226624879595063154e-21 pi/2 - (pio2_1+pio2_2) */
	static private final double pio2_3  = Double.longBitsToDouble(0x3ba3198a2e000000L);  /* 2.02226624871116645580e-21 third  33 bit of pi/2 */
	static private final double pio2_3t = Double.longBitsToDouble(0x397b839a252049c1L);  /* 8.47842766036889956997e-32 pi/2 - (pio2_1+pio2_2+pio2_3) */


	/*
	 *	Return the remainder of x % pi/2 in y[0]+y[1]
	 */
	static private int __ieee754_rem_pio2(double x, double y[])
	{
		double	z = zero, w, t, r, fn;
		double	tx[] = new double[3];
		int		i, j, nx, n, ix, hx;

		hx = __HI(x);		/* high word of x */
		ix = hx&0x7fffffff;
		if (ix <= 0x3fe921fb) {
			/* |x| ~<= pi/4 , no need for reduction */
			y[0] = x;
			y[1] = 0;
			return 0;
		}

		if (ix < 0x4002d97c) {
			/* |x| < 3pi/4, special case with n=+-1 */
			if (hx > 0) {
				z = x - pio2_1;
				if (ix != 0x3ff921fb) { 	/* 33+53 bit pi is good enough */
					y[0] = z - pio2_1t;
					y[1] = (z-y[0])-pio2_1t;
				} else {		/* near pi/2, use 33+33+53 bit pi */
					z -= pio2_2;
					y[0] = z - pio2_2t;
					y[1] = (z-y[0])-pio2_2t;
				}
				return 1;
			} else {	/* negative x */
				z = x + pio2_1;
				if (ix != 0x3ff921fb) { 	/* 33+53 bit pi is good enough */
					y[0] = z + pio2_1t;
					y[1] = (z-y[0])+pio2_1t;
				} else {		/* near pi/2, use 33+33+53 bit pi */
					z += pio2_2;
					y[0] = z + pio2_2t;
					y[1] = (z-y[0])+pio2_2t;
				}
				return -1;
			}
		}

		if (ix <= 0x413921fb) { /* |x| ~<= 2^19*(pi/2), medium size */
			t  = abs(x);
			n  = (int) (t*invpio2+half);
			fn = (double)n;
			r  = t-fn*pio2_1;
			w  = fn*pio2_1t;	/* 1st round good to 85 bit */
			if (n<32&&ix!=npio2_hw[n-1]) {	
				y[0] = r-w;	/* quick check no cancellation */
			} else {
				j  = ix>>20;
				y[0] = r-w; 
				i = j-(((__HI(y[0]))>>20)&0x7ff);
				if (i>16) {  /* 2nd iteration needed, good to 118 */
					t  = r;
					w  = fn*pio2_2;	
					r  = t-w;
					w  = fn*pio2_2t-((t-r)-w);	
					y[0] = r-w;
					i = j-(((__HI(y[0]))>>20)&0x7ff);
					if (i>49)  {	/* 3rd iteration need, 151 bits acc */
						t  = r;	/* will cover all possible cases */
						w  = fn*pio2_3;	
						r  = t-w;
						w  = fn*pio2_3t-((t-r)-w);	
						y[0] = r-w;
					}
				}
			}
			y[1] = (r-y[0])-w;
			if (hx<0) {
				y[0] = -y[0];
				y[1] = -y[1];
				return -n;
			} else {
				return n;
			}
		}

	    /* 
		 * all other (large) arguments
		*/
		if (ix >= 0x7ff00000) {
			/* x is inf or NaN */
			y[0] = y[1] = x-x;
			return 0;
		}
		
		/* set z = scalbn(|x|,ilogb(x)-23) */
		long lx = Double.doubleToLongBits(x);
		long exp = (0x7ff0000000000000L&lx) >> 52;
		exp -= 1046;
		lx -= (exp<<52);
		lx &= 0x7fffffffffffffffL;
		z = Double.longBitsToDouble(lx);
		for (i = 0;  i < 2;  i++) {
			tx[i] = (double)((int)(z));
			z     = (z-tx[i])*two24;
		}
		tx[2] = z;
		nx = 3;
		while (tx[nx-1] == zero) nx--;	/* skip zero term */
		n = __kernel_rem_pio2(tx, y, (int)exp, nx);
		//System.out.println("KERNEL");
		//System.out.println("tx "+tx[0]+"  "+tx[1]+"  "+tx[2]);
		//System.out.println("y "+y[0]+"  "+y[1]);
		//System.out.println("exp "+(int)exp+"  nx "+nx+"   n "+n);
		if (hx < 0) {
			y[0] = -y[0];
			y[1] = -y[1];
			return -n;
		}
		return n;
	}


	/*
	 * __kernel_rem_pio2(x,y,e0,nx)
	 * double x[],y[]; int e0,nx; int two_over_pi[];
	 * 
	 * __kernel_rem_pio2 return the last three digits of N with 
	 *		y = x - N*pi/2
	 * so that |y| < pi/2.
	 *
	 * The method is to compute the integer (mod 8) and fraction parts of 
	 * (2/pi)*x without doing the full multiplication. In general we
	 * skip the part of the product that are known to be a huge integer
	 * (more accurately, = 0 mod 8 ). Thus the number of operations are
	 * independent of the exponent of the input.
	 *
	 * (2/pi) is represented by an array of 24-bit integers in two_over_pi[].
	 *
	 * Input parameters:
	 * 	x[]	The input value (must be positive) is broken into nx 
	 *		pieces of 24-bit integers in double precision format.
	 *		x[i] will be the i-th 24 bit of x. The scaled exponent 
	 *		of x[0] is given in input parameter e0 (i.e., x[0]*2^e0 
	 *		match x's up to 24 bits.
	 *
	 *		Example of breaking a double positive z into x[0]+x[1]+x[2]:
	 *			e0 = ilogb(z)-23
	 *			z  = scalbn(z,-e0)
	 *		for i = 0,1,2
	 *			x[i] = floor(z)
	 *			z    = (z-x[i])*2**24
	 *
	 *
	 *	y[]	ouput result in an array of double precision numbers.
	 *		The dimension of y[] is:
	 *			24-bit  precision	1
	 *			53-bit  precision	2
	 *			64-bit  precision	2
	 *			113-bit precision	3
	 *		The actual value is the sum of them. Thus for 113-bit
	 *		precison, one may have to do something like:
	 *
	 *		long double t,w,r_head, r_tail;
	 *		t = (long double)y[2] + (long double)y[1];
	 *		w = (long double)y[0];
	 *		r_head = t+w;
	 *		r_tail = w - (r_head - t);
	 *
	 *	e0	The exponent of x[0]
	 *
	 *	nx	dimension of x[]
	 *
	 *  	prec	an integer indicating the precision:
	 *			0	24  bits (single)
	 *			1	53  bits (double)
	 *			2	64  bits (extended)
	 *			3	113 bits (quad)
	 *
	 *	two_over_pi[]
	 *		integer array, contains the (24*i)-th to (24*i+23)-th 
	 *		bit of 2/pi after binary point. The corresponding 
	 *		floating value is
	 *
	 *			two_over_pi[i] * 2^(-24(i+1)).
	 *
	 * External function:
	 *	double scalbn(), floor();
	 *
	 *
	 * Here is the description of some local variables:
	 *
	 * 	jk	jk+1 is the initial number of terms of two_over_pi[] needed
	 *		in the computation. The recommended value is 2,3,4,
	 *		6 for single, double, extended,and quad.
	 *
	 * 	jz	local integer variable indicating the number of 
	 *		terms of two_over_pi[] used. 
	 *
	 *	jx	nx - 1
	 *
	 *	jv	index for pointing to the suitable two_over_pi[] for the
	 *		computation. In general, we want
	 *			( 2^e0*x[0] * two_over_pi[jv-1]*2^(-24jv) )/8
	 *		is an integer. Thus
	 *			e0-3-24*jv >= 0 or (e0-3)/24 >= jv
	 *		Hence jv = max(0,(e0-3)/24).
	 *
	 *	jp	jp+1 is the number of terms in PIo2[] needed, jp = jk.
	 *
	 * 	q[]	double array with integral value, representing the
	 *		24-bits chunk of the product of x and 2/pi.
	 *
	 *	q0	the corresponding exponent of q[0]. Note that the
	 *		exponent for q[i] would be q0-24*i.
	 *
	 *	PIo2[]	double precision array, obtained by cutting pi/2
	 *		into 24 bits chunks. 
	 *
	 *	f[]	two_over_pi[] in floating point 
	 *
	 *	iq[]	integer array by breaking up q[] in 24-bits chunk.
	 *
	 *	fq[]	final product of x*(2/pi) in fq[0],..,fq[jk]
	 *
	 *	ih	integer. If >0 it indicates q[] is >= 0.5, hence
	 *		it also indicates the *sign* of the result.
	 *
	 */

	/*
	 * Constants:
	 * The hexadecimal values are the intended ones for the following 
	 * constants. The decimal values may be used, provided that the 
	 * compiler will convert from decimal to binary accurately enough 
	 * to produce the hexadecimal values shown.
	 */

	static final private double PIo2[] = {
		Double.longBitsToDouble(0x3ff921fb40000000L),  /* 1.57079625129699707031e+00 */
		Double.longBitsToDouble(0x3e74442d00000000L),  /* 7.54978941586159635335e-08 */
		Double.longBitsToDouble(0x3cf8469880000000L),  /* 5.39030252995776476554e-15 */
		Double.longBitsToDouble(0x3b78cc5160000000L),  /* 3.28200341580791294123e-22 */
		Double.longBitsToDouble(0x39f01b8380000000L),  /* 1.27065575308067607349e-29 */
		Double.longBitsToDouble(0x387a252040000000L),  /* 1.22933308981111328932e-36 */
		Double.longBitsToDouble(0x36e3822280000000L),  /* 2.73370053816464559624e-44 */
		Double.longBitsToDouble(0x3569f31d00000000L)   /* 2.16741683877804819444e-51 */
	};

	static final private double twon24 = Double.longBitsToDouble(0x3E70000000000000L);  /* 5.96046447753906250000e-08 */

	static private int __kernel_rem_pio2(double x[], double y[], int e0, int nx)
	{
		int		jz,jx,jv,jp,jk,carry,n,i,j,k,m,q0,ih;
		double	z,fw;
		double	f[] = new double[20];
		double	q[] = new double[20];
		double	fq[] = new double[20];
		int		iq[] = new int[20];

		/* initialize jk*/
		jk = 4;
		jp = jk;
		
		/* determine jx,jv,q0, note that 3>q0 */
		jx =  nx - 1;
		jv = (e0-3)/24;
		if (jv < 0)  jv = 0;
		q0 =  e0-24*(jv+1);
		
		/* set up f[0] to f[jx+jk] where f[jx+jk] = two_over_pi[jv+jk] */
		j = jv - jx;
		m = jx + jk;
		for (i = 0;  i <= m;  i++ ,j++)
			f[i] = ((j<0) ? zero : (double)two_over_pi[j]);

		/* compute q[0],q[1],...q[jk] */
		for (i = 0;  i <= jk;  i++) {
			for (j = 0, fw = 0.0;  j <= jx;  j++)
				fw += x[j]*f[jx+i-j];
			q[i] = fw;
		}
		
		jz = jk;
		
		while (true) {	// recompute:
			/* distill q[] into iq[] reversingly */
			for (i = 0, j = jz, z = q[jz];  j > 0;  i++, j--) {
				fw    =  (double)((int)(twon24* z));
				iq[i] =  (int)(z-two24*fw);
				z     =  q[j-1]+fw;
			}

		/* compute n */
			z  = scalbn(z, q0);		/* actual value of z */
			z -= 8.0*floor(z*0.125);		/* trim off integer >= 8 */
			n  = (int) z;
			z -= (double)n;
			ih = 0;
			if (q0 > 0) {	/* need iq[jz-1] to determine n */
				i  = (iq[jz-1]>>(24-q0));
				n += i;
				iq[jz-1] -= i<<(24-q0);
				ih = iq[jz-1]>>(23-q0);
			} else if (q0==0) {
				ih = iq[jz-1]>>23;
			} else if(z>=0.5) {
				ih=2;
			}
			if (ih>0) {	/* q > 0.5 */
				n += 1;
				carry = 0;
				for(i=0;i<jz ;i++) {	/* compute 1-q */
					j = iq[i];
					if (carry == 0) {
						if (j != 0) {
							carry = 1;
							iq[i] = 0x1000000- j;
						}
					} else  iq[i] = 0xffffff - j;
				}
				if (q0 > 0) {		/* rare case: chance is 1 in 12 */
					switch (q0) {
					case 1:
						iq[jz-1] &= 0x7fffff; break;
					case 2:
						iq[jz-1] &= 0x3fffff; break;
					}
				}
				if (ih == 2) {
					z = one - z;
					if (carry != 0) z -= scalbn(one,q0);
				}
			}

			/* check if recomputation is needed */
			if (z == zero) {
				j = 0;
				for (i = jz-1;  i >= jk;  i--)
					j |= iq[i];
				if (j == 0) { /* need recomputation */
					for (k = 1;  iq[jk-k] == 0;  k++);   /* k = no. of terms needed */
					for (i = jz+1;  i <= jz+k;  i++) {   /* add q[jz+1] to q[jz+k] */
						f[jx+i] = (double) two_over_pi[jv+i];
						for (j = 0, fw = 0.0;  j <= jx;  j++)
							fw += x[j]*f[jx+i-j];
						q[i] = fw;
					}
					jz += k;
					continue;  //goto recompute;
				}
			}
			break;
		}

		/* chop off zero terms */
		if (z == 0.0) {
			jz--;
			q0 -= 24;
			while (iq[jz] == 0) {
				jz--;
				q0 -= 24;
			}
		} else { /* break z into 24-bit if necessary */
			z = scalbn(z,-q0);
			if (z >= two24) {
				fw = (double)((int)(twon24*z));
				iq[jz] = (int)(z-two24*fw);
				jz++;
				q0 += 24;
				iq[jz] = (int)fw;
			} else iq[jz] = (int)z;
		}

		/* convert integer "bit" chunk to floating-point value */
		fw = scalbn(one, q0);
		for (i = jz;  i >= 0;  i--) {
			q[i] = fw*(double)iq[i]; fw*=twon24;
		}

		/* compute PIo2[0,...,jp]*q[jz,...,0] */
		for (i = jz;  i >= 0;  i--) {
			for (fw = 0.0, k = 0;  k <= jp && k <= jz-i;  k++)
				fw += PIo2[k]*q[i+k];
			fq[jz-i] = fw;
		}
		
		/* compress fq[] into y[] */
		fw = 0.0;
		for (i = jz;  i >= 0;  i--)
			fw += fq[i]; 
		y[0] = (ih==0)? fw: -fw; 
		fw = fq[0]-fw;
		for (i = 1;  i <= jz;  i++)
			fw += fq[i];
		y[1] = ((ih==0) ? fw: -fw); 
		return n&7;
	}


	static final private double bp[] = {1.0, 1.5,};
	static final private double dp_h[] = { 0.0, Double.longBitsToDouble(0x3fe2b80340000000L)};  /* 5.84962487220764160156e-01 */
	static final private double dp_l[] = { 0.0, Double.longBitsToDouble(0x3e4cfdeb43cfd006L)};  /* 1.35003920212974897128e-08 */
	static final private double two53  =  Double.longBitsToDouble(0x4340000000000000L);  /* 9007199254740992.0 */
	/* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */
	static final private double L1  = Double.longBitsToDouble(0x3fe3333333333303L);  /* 5.99999999999994648725e-01 */
	static final private double L2  = Double.longBitsToDouble(0x3fdb6db6db6fabffL);  /*  4.28571428578550184252e-01 */
	static final private double L3  = Double.longBitsToDouble(0x3fd55555518f264dL);  /*  3.33333329818377432918e-01 */
	static final private double L4  = Double.longBitsToDouble(0x3fd17460a91d4101L);  /*  2.72728123808534006489e-01 */
	static final private double L5  = Double.longBitsToDouble(0x3fcd864a93c9db65L);  /*  2.30660745775561754067e-01 */
	static final private double L6  = Double.longBitsToDouble(0x3fca7e284a454eefL);  /*  2.06975017800338417784e-01 */
	static final private double lg2  = Double.longBitsToDouble(0x3fe62e42fefa39efL);  /*  6.93147180559945286227e-01 */
	static final private double lg2_h = Double.longBitsToDouble(0x3fe62e4300000000L);  /*  6.93147182464599609375e-01 */
	static final private double lg2_l = -1.90465429995776804525e-09; /* 0xbe205c610ca86c39 */
	static final private double ovt  = 8.0085662595372944372e-17; /* -(1024-log2(ovfl+.5ulp)) */
	static final private double cp   = Double.longBitsToDouble(0x3feec709dc3a03fdL);  /*  9.61796693925975554329e-01 = 2/(3ln2) */
	static final private double cp_h = Double.longBitsToDouble(0x3feec709e0000000L);  /*  9.61796700954437255859e-01 = (float)cp */
	static final private double cp_l = Double.longBitsToDouble(0xbe3e2fe0145b01f5L);  /* -7.02846165095275826516e-09 = tail of cp_h*/
	static final private double ivln2   = Double.longBitsToDouble(0x3ff71547652b82feL);  /*  1.44269504088896338700e+00 = 1/ln2 */
	static final private double ivln2_h = Double.longBitsToDouble(0x3ff7154760000000L);  /*  1.44269502162933349609e+00 = 24b 1/ln2*/
	static final private double ivln2_l = Double.longBitsToDouble(0x3e54ae0bf85ddf44L);  /*  1.92596299112661746887e-08 = 1/ln2 tail*/


	/*
	 *	Returns x to the power y
	 *
	 *		      n
	 * Method:  Let x =  2   * (1+f)
	 *	1. Compute and return log2(x) in two pieces:
	 *		log2(x) = w1 + w2,
	 *	   where w1 has 53-24 = 29 bit trailing zeros.
	 *	2. Perform y*log2(x) = n+y' by simulating muti-precision 
	 *	   arithmetic, where |y'|<=0.5.
	 *	3. Return x**y = 2**n*exp(y'*log2)
	 *
	 * Special cases:
	 *	1.  (anything) ** 0  is 1
	 *	2.  (anything) ** 1  is itself
	 *	3.  (anything) ** NAN is NAN
	 *	4.  NAN ** (anything except 0) is NAN
	 *	5.  +-(|x| > 1) **  +INF is +INF
	 *	6.  +-(|x| > 1) **  -INF is +0
	 *	7.  +-(|x| < 1) **  +INF is +0
	 *	8.  +-(|x| < 1) **  -INF is +INF
	 *	9.  +-1         ** +-INF is NAN
	 *	10. +0 ** (+anything except 0, NAN)               is +0
	 *	11. -0 ** (+anything except 0, NAN, odd integer)  is +0
	 *	12. +0 ** (-anything except 0, NAN)               is +INF
	 *	13. -0 ** (-anything except 0, NAN, odd integer)  is +INF
	 *	14. -0 ** (odd integer) = -( +0 ** (odd integer) )
	 *	15. +INF ** (+anything except 0,NAN) is +INF
	 *	16. +INF ** (-anything except 0,NAN) is +0
	 *	17. -INF ** (anything)  = -0 ** (-anything)
	 *	18. (-anything) ** (integer) is (-1)**(integer)*(+anything**integer)
	 *	19. (-anything except 0 and inf) ** (non-integer) is NAN
	 *
	 * Accuracy:
	 *	pow(x,y) returns x**y nearly rounded. In particular
	 *			pow(integer,integer)
	 *	always returns the correct integer provided it is 
	 *	representable.
	 */

	/**
	 *	Returns x to the power y.
	 *	@param	x	The base.
	 *	@param	y	The exponent.
	 *	@return	x to the power y.
	 */
	static public double pow(double x, double y)
	{
		double	z, ax, z_h, z_l, p_h, p_l;
		double	y1, t1, t2, r, s, t, u, v, w;
		int		i, j, k, yisint, n;
		int		hx, hy, ix, iy;
		int		lx, ly;
		
		hx = __HI(x);
		lx = __LO(x);
		hy = __HI(y);
		ly = __LO(y);
		ix = hx & 0x7fffffff;
		iy = hy & 0x7fffffff;
		
		/* y==zero: x**0 = 1 */
		if ((iy|ly) == 0)  return one;

		/* +-NaN return x+y */
		if (ix > 0x7ff00000 || ((ix==0x7ff00000)&&(lx!=0)) ||
			iy > 0x7ff00000 || ((iy==0x7ff00000)&&(ly!=0))) 
			return x+y;	

		/* determine if y is an odd int when x < 0
		 * yisint = 0	... y is not an integer
		 * yisint = 1	... y is an odd int
		 * yisint = 2	... y is an even int
		 */
		yisint  = 0;
		if (hx < 0) {	
			if (iy >= 0x43400000)
				yisint = 2; /* even integer y */
			else if(iy >= 0x3ff00000) {
				k = (iy>>20)-0x3ff;	   /* exponent */
				if (k > 20) {
					j = ly>>>(52-k);
					if ((j<<(52-k)) == ly)
						yisint = 2-(j&1);
				} else if (ly == 0) {
					j = iy >> (20-k);
					if ((j<<(20-k)) == iy)
						yisint = 2-(j&1);
				}
			}
		}

		/* special value of y */
		if (ly==0) {
			if (iy == 0x7ff00000) {	/* y is +-inf */
				if (((ix-0x3ff00000)|lx) == 0)
					return  y - y;	/* inf**+-1 is NaN */
				else if (ix >= 0x3ff00000)/* (|x|>1)**+-inf = inf,0 */
					return (hy>=0)? y: zero;
				else			/* (|x|<1)**-,+inf = inf,0 */
					return (hy<0)?-y: zero;
			} 
			if (iy == 0x3ff00000) {	/* y is  +-1 */
				if (hy < 0)
					return one/x;
				else
					return x;
			}
			if (hy == 0x40000000)
				return x*x; /* y is  2 */
			if (hy == 0x3fe00000) {	/* y is  0.5 */
				if(hx>=0)	/* x >= +0 */
					return sqrt(x);	
			}
		}
		
		ax   = abs(x);
		/* special value of x */
		if (lx == 0) {
			if (ix==0x7ff00000 || ix==0 || ix==0x3ff00000) {
				z = ax;			/*x is +-0,+-inf,+-1*/
				if (hy < 0 )
					z = one/z;	/* z = (1/|x|) */
				if (hx < 0) {
					if (((ix-0x3ff00000)|yisint) == 0) {
						z = (z-z)/(z-z); /* (-1)**non-int is NaN */
					} else if (yisint==1) 
						z = -z;		/* (x<0)**odd = -(|x|**odd) */
				}
				return z;
			}
		}
		
		/* (x<0)**(non-int) is NaN */
		if ((((hx>>31)+1)|yisint) == 0)
			return (x-x)/(x-x);
		
		/* |y| is huge */
		if (iy > 0x41e00000) { /* if |y| > 2**31 */
			if (iy > 0x43f00000){	/* if |y| > 2**64, must o/uflow */
				if (ix <= 0x3fefffff)
					return ((hy < 0) ? huge*huge : tiny*tiny);
				if (ix >= 0x3ff00000)
					return ((hy > 0) ? huge*huge : tiny*tiny);
	    }
			
		/* over/underflow if x is not close to one */
		if (ix < 0x3fefffff)
			return ((hy < 0) ? huge*huge : tiny*tiny);
		if (ix > 0x3ff00000)
			return ((hy > 0) ? huge*huge : tiny*tiny);
			/* now |1-x| is tiny <= 2**-20, suffice to compute 
		log(x) by x-x^2/2+x^3/3-x^4/4 */
		t = x-1;		/* t has 20 trailing zeros */
		w = (t*t)*(0.5-t*(0.3333333333333333333333-t*0.25));
		u = ivln2_h*t;	/* ivln2_h has 21 sig. bits */
		v = t*ivln2_l-w*ivln2;
		t1 = u+v;
		t1 = setLO(t1, 0);
		t2 = v-(t1-u);
		} else {
			double s2,s_h,s_l,t_h,t_l;
			n = 0;
			/* take care subnormal number */
			if (ix<0x00100000) {
				ax *= two53;
				n -= 53;
				ix = __HI(ax);
			}
			n  += ((ix)>>20) - 0x3ff;
			j  = ix & 0x000fffff;
			/* determine interval */
			ix = j|0x3ff00000;		/* normalize ix */
			if (j <= 0x3988E)
				k=0;		/* |x|<sqrt(3/2) */
			else if (j < 0xBB67A)
				k=1;	/* |x|<sqrt(3)   */
			else {
				k = 0;
				n+=1;
				ix -= 0x00100000;
			}
			ax = setHI(ax, ix);
			
			/* compute s = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
			u = ax-bp[k];		/* bp[0]=1.0, bp[1]=1.5 */
			v = one/(ax+bp[k]);
			s = u*v;
			s_h = s;
			s_h = setLO(s_h, 0);
			/* t_h=ax+bp[k] High */
			t_h = zero;
			t_h = setHI(t_h, ((ix>>1)|0x20000000)+0x00080000+(k<<18)); 
			t_l = ax - (t_h-bp[k]);
			s_l = v*((u-s_h*t_h)-s_h*t_l);
			/* compute log(ax) */
			s2 = s*s;
			r = s2*s2*(L1+s2*(L2+s2*(L3+s2*(L4+s2*(L5+s2*L6)))));
			r += s_l*(s_h+s);
			s2  = s_h*s_h;
			t_h = 3.0+s2+r;
			t_h = setLO(t_h, 0);
			t_l = r-((t_h-3.0)-s2);
			/* u+v = s*(1+...) */
			u = s_h*t_h;
			v = s_l*t_h+t_l*s;
			/* 2/(3log2)*(s+...) */
			p_h = u+v;
			p_h = setLO(p_h, 0);
			p_l = v-(p_h-u);
			z_h = cp_h*p_h;		/* cp_h+cp_l = 2/(3*log2) */
			z_l = cp_l*p_h+p_l*cp+dp_l[k];
			/* log2(ax) = (s+..)*2/(3*log2) = n + dp_h + z_h + z_l */
			t = (double)n;
			t1 = (((z_h+z_l)+dp_h[k])+t);
			t1 = setLO(t1, 0);
			t2 = z_l-(((t1-t)-dp_h[k])-z_h);
		}
		
		s = one; /* s (sign of result -ve**odd) = -1 else = 1 */
		if((((hx>>31)+1)|(yisint-1))==0) s = -one;/* (-ve)**(odd int) */

		/* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */
		y1  = y;
		y1 = setLO(y1, 0);
		p_l = (y-y1)*t1+y*t2;
		p_h = y1*t1;
		z = p_l+p_h;
		j = __HI(z);
		i = __LO(z);
		if (j >= 0x40900000) {				/* z >= 1024 */
			if (((j-0x40900000)|i) != 0)	/* if z > 1024 */
				return s*huge*huge;			/* overflow */
			else {
				if (p_l+ovt > z-p_h)
					return s*huge*huge;	/* overflow */
			}
		} else if((j&0x7fffffff) >= 0x4090cc00) {	/* z <= -1075 */
			if (((j-0xc090cc00)|i) != 0) 		/* z < -1075 */
				return s*tiny*tiny;		/* underflow */
			else {
				if (p_l <= z-p_h) return s*tiny*tiny;	/* underflow */
			}
		}
		/*
		 * compute 2**(p_h+p_l)
		 */
		i = j&0x7fffffff;
		k = (i>>20)-0x3ff;
		n = 0;
		if (i > 0x3fe00000) {		/* if |z| > 0.5, set n = [z+0.5] */
			n = j + (0x00100000>>(k+1));
			k = ((n&0x7fffffff)>>20) - 0x3ff;	/* new k for n */
			t = zero;
			t = setHI(t, (n&~(0x000fffff>>k)));
			n = ((n&0x000fffff)|0x00100000)>>(20-k);
			if (j < 0) n = -n;
			p_h -= t;
		} 
		t = p_l + p_h;
		t = setLO(t,0);
		u = t*lg2_h;
		v = (p_l-(t-p_h))*lg2 + t*lg2_l;
		z = u + v;
		w = v - (z-u);
		t = z*z;
		t1= z - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
		r = (z*t1)/(t1-2.0) - (w+z*w);
		z = one - (r-z);
		j = __HI(z);
		j += (n<<20);
		if ((j>>20) <= 0) {
			z = scalbn(z,n);	/* subnormal output */
		} else {
			i = __HI(z);
			i += (n << 20);
			z = setHI(z, i);
		}
		return s*z;
	}


/*
 * copysign(double x, double y)
 * copysign(x,y) returns a value with the magnitude of x and
 * with the sign bit of y.
 */

	static private double copysign(double x, double y)
	{
		long ix = Double.doubleToLongBits(x);
		long iy = Double.doubleToLongBits(y);
		ix = (0x7fffffffffffffffL*ix) | (0x8000000000000000L&iy);
		return Double.longBitsToDouble(ix);
	}

	static private final double two54  = Double.longBitsToDouble(0x4350000000000000L);  /*  1.80143985094819840000e+16 */
	static private final double twom54 = Double.longBitsToDouble(0x3c90000000000000L);  /*  5.55111512312578270212e-17 */


	/* 
	 * scalbn (double x, int n)
	 * scalbn(x,n) returns x* 2**n  computed by  exponent  
	 * manipulation rather than by actually performing an 
	 * exponentiation or a multiplication.
	 */
	static private double scalbn (double x, int n)
	{
		int  k, hx, lx;
		hx = __HI(x);
		lx = __LO(x);
        k = (hx&0x7ff00000)>>20;		/* extract exponent */
        if (k == 0) {				/* 0 or subnormal x */
            if ((lx|(hx&0x7fffffff))==0) return x; /* +-0 */
			x *= two54; 
			hx = __HI(x);
			k = ((hx&0x7ff00000)>>20) - 54; 
            if (n < -50000) return tiny*x; 	/*underflow*/
		}
        if (k == 0x7ff) return x+x;		/* NaN or Inf */
        k = k+n; 
        if (k >  0x7fe) return huge*copysign(huge,x); /* overflow  */
        if (k > 0) {
			/* normal result */
			return setHI(x, (hx&0x800fffff)|(k<<20));
		}
        if (k <= -54) {
            if (n > 50000) 	/* in case integer overflow in n+k */
				return huge*copysign(huge,x);	/*overflow*/
		} else {
			return tiny*copysign(tiny,x); 	/*underflow*/
		}
        k += 54;				/* subnormal result */
        return twom54 * setHI(x, (hx&0x800fffff)|(k<<20));
	}


	static private double set(int newHiPart, int newLowPart)
	{
		return Double.longBitsToDouble((((long)newHiPart)<<32) | newLowPart);
	}


	static private double setLO(double x, int newLowPart)
	{
		long	lx = Double.doubleToLongBits(x);
		lx &= 0xFFFFFFFF00000000L;
		lx |= newLowPart;
		return Double.longBitsToDouble(lx);
	}


	static private double setHI(double x, int newHiPart)
	{
		long	lx = Double.doubleToLongBits(x);
		lx &= 0x00000000FFFFFFFFL;
		lx |= (((long)newHiPart)<<32);
		return Double.longBitsToDouble(lx);
	}

	static private int __HI(double x)
	{
		return (int)(0xFFFFFFFF&(Double.doubleToLongBits(x)>>32));
	}

	static private int __LO(double x)
	{
		return (int)(0xFFFFFFFF&Double.doubleToLongBits(x));
	}

}
